This Thesis investigates the design of Ge-on-Si single-photon avalanche diode (SPAD) detectors combining the many advantages of low-noise Si single-photon avalanche multiplication with the infrared sensing capability of germanium. The devices were simulated by using electric field modelling software to predict key aspects of the device behaviour in terms of the current-voltage characteristic and electric field. The devices were then characterised in terms of their single-photon performance. A 25 m diameter device showed a single-photon detection efficiency of ~ 4 % at a wavelength of 1310 nm and a temperature of 100 K when biased at 10 % above the breakdown voltage. In the same condition, a dark count rate of ~ 6 Mcs-1 was measured. This resulted in the lowest noise equivalent power of ~ 1 × 10-14 WHz-1/2 of Ge-on-Si SPADs reported in the scientific literature. At the longer wavelength of 1550 nm, the single-photon detection efficiency was reduced to ~ 0.1 % at 125 K and 6 % of relative excess bias. Although further investigation needs to be carried out, a potential major advantage of these devices compared to the InGaAs/InP SPADs could be that of reduced afterpulsing since a small increase (a factor of 2) in the normalised dark count rate was measured when the repetition rate was increased from 1 kHz to 1 MHz. Finally, the fill-factor enhancement of 32 × 32 Si CMOS SPAD arrays resulting from the integration of high efficiency diffractive optical microlens arrays was investigated. A full characterisation of SPAD arrays integrating microlens arrays in terms of improvement factor and spatial uniformity of detection is presented for the first time in the scientific literature in a large spectral range (500-900 nm) and different f-numbers (from f/2 to f/22) by using a double telecentric imaging system. The highest improvement factor of ~16 was measured for a SPAD array integrating microlens arrays, combined with a very high spatial efficiency uniformity of between 2–6%.